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通过能量法和Hamilton原理,建立径向均布周期荷载作用下闭口薄壁截面圆弧拱动力稳定偏微分方程,利用Galerkin方法将其转化为2阶常微分Mathieu-Hill型参数振动方程,求得周期解所包围的动力不稳定区域,探讨了闭口截面圆弧拱发生空间参数振动的动力稳定性问题,分析了恒载系数、圆弧半径以及圆心角等参数对空间动力不稳定区域的影响,为工程结构动力设计提供参考依据。 相似文献
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考虑剪切变形的薄壁杆件稳定分析 总被引:6,自引:1,他引:5
本文提出了一种基于势能原理的薄壁杆件稳定分析的半离散方法。采用转换B3样条函数作为横截面纵向位移的插值函数,通过变分原理,导出控制微分方程及自然边界条件,利用常微分方程求解器求解。分析时放弃了古典理论关于杆壁中线剪应变为零或剪力流为常数的假设,很好地描述了剪力滞后现象。本方法适用于任意截面形状的薄壁杆件,能够灵活、精确、有效地进行薄壁杆件在轴压与纯弯作用下的稳定分析。算例的快速收敛说明了计算结果的可靠性。 相似文献
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该文为探究铺层角度对基础竖向激励下GFRP圆弧拱平面内动力稳定性能的影响,开展了系统的实验研究。设计了6组不同铺层角度的圆弧拱试件,利用TIRA激振器模拟输出基础竖向周期激励,采用NDI三维动态采集仪采集圆弧拱的竖向动位移,根据测得拱的面内自由振动响应,分别通过快速傅里叶变换和自由衰减法获得拱的自振频率和阻尼比。通过扫频实测了GFRP拱的动力不稳定域边界,并与有限元计算结果进行对比,基本吻合。研究表明:当外部频率约为结构自身频率两倍时,结构会出现激烈的面内反对称振动现象,即为参数共振失稳;当激励加速度小于临界激发加速度时,拱处于定态振动;外激励大于临界激发加速度时,GFRP拱出现参数振动,并且随着加速度的增大,拱的振动愈发激烈;随着铺层角度的增大,拱的自振频率和临界激发加速度逐渐减小,阻尼比与不稳定域范围逐渐增大。 相似文献
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混凝土两铰圆弧拱的面内徐变稳定性 总被引:1,自引:0,他引:1
结合两铰圆弧拱的面内屈曲微分方程和混凝土徐变的Arutyunyan-Maslov方程,并引入徐变积分算子和失稳条件推导了混凝土两铰圆弧拱的面内徐变临界力计算公式。基于该公式,通过算例讨论了徐变系数和截面含钢率对徐变临界力的影响,并对素混凝土拱、钢筋混凝土拱和钢管混凝土拱的徐变临界力进行了对比。结果表明:对于不同拱肋材料,混凝土徐变均会导致临界力的降低;由于材料组成的差别,徐变对素混凝土拱临界力的影响最大,钢筋混凝土拱次之,而对钢管混凝土拱的影响最小;与已有方法相比,该公式反映了截面配筋率或含钢率对徐变临界力的影响。 相似文献
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首先利用线性的动力屈曲方程,对受压的理想圆柱壳稳定性进行了动力分析。接着利用随时间周期变化的轴压载荷,导出Mathieu方程,讨论了轴压柱壳的参数共振。在Donnell-K偄rm偄n大挠度方程中引入惯性力和阻尼力给出圆柱壳的非线性运动方程,借助Bubnov-Galerkin法,将其转化为含有三次非线性的常微分方程。在定性分析的基础上,利用次谐轨道Melnikov函数和同宿轨道的Melnikov函数分别给出了前屈曲和后屈曲情况下发生Smale马蹄型混沌的临界条件。在此基础上,选用适当参数借用MATLAB数学软件,计算运动时程曲线、相图和Poincar啨映射,给出了混沌运动的数字特征。 相似文献
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This work presents an analytical solution for acoustic transmission through relatively thick FGM cylindrical shells using third order shear deformation theory (TSDT). An infinitely long FGM cylindrical shell composed of metal and ceramic with power-law distribution of volume fraction through the thickness is considered. The shell is immersed in a fluid with an external airflow and an oblique plane wave impinges on the external sidewall of the shell. Comparing the results of present study with those of previous models (CST and FSDT) for thin shells, similar results are observed due to limited effects of shear and rotation on transmission loss (TL). However, for relatively thick shells where the shear and rotation effects become more important in lower R/h, TSDT presents more accurate results caused by its higher order model. In addition, the results show proportional change in TL according to distribution of material properties through the thickness of FG cylindrical shells. 相似文献
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An analysis of the stability of circular cylindrical columns/beams composed of functionally graded materials is made where shear deformation is taken into account. In this study, a new approach is carried out. Different from the assumption of uniform shear stress at the cross-section adopted in the Timoshenko beam theory, proposed model provides a new approach for treating the problem. Based on the traction-free surface condition, two coupled governing equations for the deflection and rotation are derived, and a single governing equation is further obtained. A comparison of buckling loads derived from the proposed circular column model and the Timoshenko and Euler–Bernoulli theories of beams is made. Moreover, the effects of radial gradient on buckling loads of elastic columns with circular cross-section made of functionally graded materials are elucidated. Finally, the stability of double-walled carbon nanotubes is considered and critical stress is determined and compared with existing results. The results obtained by the proposed model show very good agreement with the results of the Timoshenko beam theory or Reddy–Bickford beam theory. 相似文献
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Da-Guang Zhang 《先进材料力学与结构力学》2017,24(2):142-148
Thermal post-buckling analysis is first presented for functionally graded elliptical plates based on high-order shear deformation theory in different thermal environments. Material properties are assumed to be temperature-dependent and graded in the thickness direction. Ritz method is employed to determine the central deflection-temperature curves, the validity of which can be confirmed by comparison with related researchers' results; it is worth noting that the forms of approximate solutions are well chosen in consideration of both simplicity and accuracy. Influences played by different supported boundaries, thermal environmental conditions, ratio of major to minor axis, and volume fraction index are discussed in detail. 相似文献
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Small scale effects in the functionally graded beam are investigated by using various nonlocal higher-order shear deformation beam theories. The material properties of a beam are supposed to vary according to power law distribution of the volume fraction of the constituents. The nonlocal equilibrium equations are obtained and an exact solution is presented for vibration analysis of functionally graded (FG) nanobeams. The accuracy of the present model is discussed by comparing the results with previous studies and a parametric investigation is presented to study the effects of power law index, small-scale parameter, and aspect ratio on the vibrational behavior of FG nanostructures. 相似文献
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Buckling analysis of corrugated plates using a mesh-free Galerkin method based on the first-order shear deformation theory 总被引:1,自引:0,他引:1
This paper deals with elastic buckling analysis of stiffened and un-stiffened corrugated plates via a mesh-free Galerkin method
based on the first-order shear deformation theory (FSDT). The corrugated plates are approximated by orthotropic plates of
uniform thickness that have different elastic properties along the two perpendicular directions of the plates. The key to
the approximation is that the equivalaent elastic properties of the orthotropic plates are derived by applying constant curvature
conditions to the corrugated sheet. The stiffened corrugated plates are analyzed as stiffened orthotropic plates. The stiffeners
are modelled as beams. The stiffness matrix of the stiffened corrugated plate is obtained by superimposing the strain energy
of the equivalent orthotropic plate and the beams after implementing the displacement compatibility conditions between the
plate and the beams. The mesh free characteristic of the proposed method guarantee that the stiffeners can be placed anywhere
on the plate, and that remeshing is avoided when the stiffener positions change. A few selected examples are studied to demonstrate
the accuracy and convergence of the proposed method. The results obtained for these examples, when possible, are compared
with the ANSYS solutions or other available solutions in literature. Good agreement is evident for all cases. Some new results
for both trapezoidally and sinusoidally corrugated plates are then reported. 相似文献
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In this study, free vibration of beams with different boundary conditions is analysed within the framework of the third-order
shear deformation theory. The boundary conditions of beams are satisfied using Lagrange multipliers. To apply the Lagrange’s
equations, trial functions denoting the deflections and the rotations of the cross-section of the beam are expressed in polynomial
form. Using Lagrange’s equations, the problem is reduced to the solution of a system of algebraic equations. The first six
eigenvalues of the considered beams are calculated for different thickness-to-length ratios. The results are compared with
the previous results based on Timoshenko and Euler-Bernoulli beam theories. 相似文献
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This article presents a nonlocal sinusoidal shear deformation beam theory (SDBT) for the nonlinear vibration of single-walled boron nitride nanotubes (SWBNNTs). The surrounding elastic medium is simulated based on nonlinear Pasternak foundation. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the SWBNNTs are derived using Hamilton's principle. Differential quadrature method (DQM) for the nonlinear frequency is presented, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory (TBT). The effects of nonlocal parameter, vibrational modes, length, and elastic medium on the nonlinear frequency of SWBNNTs are considered. 相似文献
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A large deformation theory, so-called Green strains with small rotations, is proposed and employed for flexural analysis of composite plates. Isogeometric analysis cooperated with first-order shear deformation theory is used to derive finite element models. Strain-displacement relations in the sense of von-Kármán theory and the proposed theory are formulated. Shear locking phenomenon is avoided by using reduced integration technique. Newton–Raphson method is employed for nonlinear analysis procedure. Numerical examples, including isotropic and laminated composite plates under different boundary conditions, are investigated. The results have been verified with those available in the literature and show the advantages of the proposed strain theory. 相似文献
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Suganyadevi Sarangan 《先进材料力学与结构力学》2018,25(15-16):1351-1360
ABSTRACTA trigonometric layerwise shear deformation theory is developed for the flexural analysis of laminated plates. The present theory achieves in-plane displacement continuity, transverse shear stress continuity, and traction-free boundary condition. Hence, botheration of shear correction coefficient is neglected. The governing differential equation and boundary conditions are obtained from the principle of virtual work. Although the present analytical method is bounded to a corner supported boundary condition, it neglects the numerical and computational error. Like first-order shear deformation theory, the present theory possesses five numbers of unknowns. Several numerical predictions are carried out and results are compared with those of other existing numerical approaches. 相似文献
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A theoretical study on the sound transmission loss (STL) characteristics of unbounded orthotropic sandwich panels considering the transverse shear deformation is presented. With the transverse shear deformation taken into account, the governing equation of bending vibration for unbounded orthotropic sandwich panels is derived and implemented to the sound transmission problem. The expressions for impedance and transmission coefficient are also derived. The accuracy of the theoretical predictions is checked against available experimental data. The influence of several key parameters on the sound insulation properties of the orthotropic sandwich panel is then systematically studied, including shear rigidity of the core, face sheet thickness, and core thickness. Numerical analysis shows that shear rigidity has evident effect on coincidence critical frequency and STL property, and should not be neglected when predicting STL. Increasing face sheet thickness can move coincidence critical frequency to lower frequency region and improve STL, which is much more effective than increasing the core thickness. 相似文献